A variety V (that is not necessarily a complete intersection) of codimension k is a component of a complete intersection of codimension k defined by k general linear combinations of any generating set of the defining ideal of V.
This function automates the above construction.
i1 : R = CC[x,y,z]; |
i2 : F = {x*y, x^2 - y, x*z}; |
i3 : L = generalEquations(2,F) 2 o3 = {(.406896 + .113203*ii)x + (.690022 + .443151*ii)x*y + (.873519 + ------------------------------------------------------------------------ 2 .567952*ii)x*z + (- .406896 - .113203*ii)y, (.692658 + .634955*ii)x + ------------------------------------------------------------------------ (.0196841 + .14935*ii)x*y + (.792396 + .109974*ii)x*z + (- .692658 - ------------------------------------------------------------------------ .634955*ii)y} o3 : List |